The circle candidates are produced by “voting” in the Hough parameter space and then selecting local maxima in an accumulator matrix.
And all the parameters that satisfy (x, y) would lie on the surface of an inverted right-angled cone whose apex is at (x, y, 0).
The first stage is fixing radius then find the optimal center of circles in a 2D parameter space.
In practice, an accumulator matrix is introduced to find the intersection point in the parameter space.
The original picture (right) is first turned into a binary image (left) using a threshold and Gaussian filter.
Since the parameter space of the CHT is three dimensional, it may require lots of storage and computation.
Since too coarse a grid can lead to large values of the vote being obtained falsely because many quite different structures correspond to a single bucket.
J. Illingworth and J. Kittler[1] introduced this method for implementing Hough Transform efficiently.
This method is substantially superior to the standard Hough Transform implementation in both storage and computational requirements.
[2] Modified Hough Circle Transform (MHCT) is used on the image extracted from Digital Subtraction Angiogram (DSA) to detect and classify aneurysms type.